Answer
$\left\{-2, 3\right\}$
Work Step by Step
RECALL:
$|x|=a \longrightarrow x=a \text{ or } x = -a$
Use the rule above to obtain:
$2x-1 = 5 \text{ or } 2x-1 = -5$
Solve each equation to obtain:
$2x = 5+1 \text{ or } 2x = -5 +1
\\2x = 6 \text{ or } 2x =-4
\\x = \frac{6}{2} \text{ or } x = \frac{-4}{2}
\\x=3 \text{ or } x = -2$
Thus, the solution set is $\left\{-2, 3\right\}$.
